Block one-step methods for solving stiff differential equations

In this research, both stiff ordinary differential equations (ODEs) and parabolic partial differential equation (PDEs) are solved using the A-stable one-step block method with Newton’s iteration with constant step size. Two-point block one-step method and three-point block one-step method had bee...

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Main Author:	Mohd Zabidi, Muhammad Izzat Zakwan
Format:	Thesis
Language:	English
Published:	2014
Subjects:	Differential equations - Numerical solutions Stiff computation (Differential equations)
Online Access:	http://psasir.upm.edu.my/id/eprint/76038/1/IPM%202014%2011%20-%20IR.pdf
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id	my-upm-ir.76038
record_format	uketd_dc
spelling	my-upm-ir.760382019-11-26T07:06:07Z Block one-step methods for solving stiff differential equations 2014-09 Mohd Zabidi, Muhammad Izzat Zakwan In this research, both stiff ordinary differential equations (ODEs) and parabolic partial differential equation (PDEs) are solved using the A-stable one-step block method with Newton’s iteration with constant step size. Two-point block one-step method and three-point block one-step method had been proposed in this research. These two methods are used to approximate the solutions for stiff ODEs and parabolic PDEs at two and three points simultaneously. The implementation of these methods will be in predictor and corrector mode. The predictor formulae is formulated from the modified block method itself. Newton’s iteration is adapted in implementation of the block methods. The order, error constant, convergence and stability of each method are also discussed. This study also focused on solving parabolic PDEs. In order to solve parabolic PDEs using the proposed methods, we reduced the form of parabolic PDEs into ODEs by discretizing the parabolic equation using method of line. To illustrate the applicability of the proposed method, several numerical results are shown and compared with the results obtained by the existing methods In conclusion, the proposed methods are suitable for solving stiff ordinary differential equations at varies stepsizes especially when the stepsizes are larger. Other than that, the proposed method also appropriate for solving stiff parabolic partial differential equations due to acceptable results that had been produced. Differential equations - Numerical solutions Stiff computation (Differential equations) 2014-09 Thesis http://psasir.upm.edu.my/id/eprint/76038/ http://psasir.upm.edu.my/id/eprint/76038/1/IPM%202014%2011%20-%20IR.pdf text en public masters Universiti Putra Malaysia Differential equations - Numerical solutions Stiff computation (Differential equations)
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Differential equations - Numerical solutions Stiff computation (Differential equations)
spellingShingle	Differential equations - Numerical solutions Stiff computation (Differential equations) Mohd Zabidi, Muhammad Izzat Zakwan Block one-step methods for solving stiff differential equations
description	In this research, both stiff ordinary differential equations (ODEs) and parabolic partial differential equation (PDEs) are solved using the A-stable one-step block method with Newton’s iteration with constant step size. Two-point block one-step method and three-point block one-step method had been proposed in this research. These two methods are used to approximate the solutions for stiff ODEs and parabolic PDEs at two and three points simultaneously. The implementation of these methods will be in predictor and corrector mode. The predictor formulae is formulated from the modified block method itself. Newton’s iteration is adapted in implementation of the block methods. The order, error constant, convergence and stability of each method are also discussed. This study also focused on solving parabolic PDEs. In order to solve parabolic PDEs using the proposed methods, we reduced the form of parabolic PDEs into ODEs by discretizing the parabolic equation using method of line. To illustrate the applicability of the proposed method, several numerical results are shown and compared with the results obtained by the existing methods In conclusion, the proposed methods are suitable for solving stiff ordinary differential equations at varies stepsizes especially when the stepsizes are larger. Other than that, the proposed method also appropriate for solving stiff parabolic partial differential equations due to acceptable results that had been produced.
format	Thesis
qualification_level	Master's degree
author	Mohd Zabidi, Muhammad Izzat Zakwan
author_facet	Mohd Zabidi, Muhammad Izzat Zakwan
author_sort	Mohd Zabidi, Muhammad Izzat Zakwan
title	Block one-step methods for solving stiff differential equations
title_short	Block one-step methods for solving stiff differential equations
title_full	Block one-step methods for solving stiff differential equations
title_fullStr	Block one-step methods for solving stiff differential equations
title_full_unstemmed	Block one-step methods for solving stiff differential equations
title_sort	block one-step methods for solving stiff differential equations
granting_institution	Universiti Putra Malaysia
publishDate	2014
url	http://psasir.upm.edu.my/id/eprint/76038/1/IPM%202014%2011%20-%20IR.pdf
_version_	1747813105623105536

Block one-step methods for solving stiff differential equations

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